Quadratic roots, wide range

Average Error: 52.2 → 6.4

Time: 5.4s

Precision: binary64

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Math

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↓

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Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Initial program 52.2

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2. Simplified 52.2

   \[\leadsto \]

3. Taylor expanded around inf 6.4

   \[\leadsto \]

4. Final simplification 6.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b c)
  :name "Quadratic roots, wide range"
  :precision binary64
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))